The tapered long-period fiber grating (TLPFG) and rotated chiral long-period fiber gratings (CLPFG) heated by a CO2 laser were fabricated by periodically tapering and rotating standard single-mode fibers (SMF). The temperature sensing characteristics of the TLPFG and CLPFG between 30 degrees C and 60 degrees C were experimentally investigated, and the slopes of the wavelength shift corresponded to 0.115 nm degrees C-1 and 0.04 nm degrees C-1, respectively. The graphene films were coated on gratings to fabricate graphene-coated TLPFG (GTLPFG) and graphene-coated CLPFG (GCLPFG). Given the thermal effects of graphene, the slopes of the resonance dip shift of the GTLPFG and GCLPFG between 30 degrees C and 60 degrees C increased to 0.196 nm degrees C-1 and 0.113 nm degrees C-1, respectively. Additionally, the high temperature sensing properties of TLPFG and CLPFG between 100 degrees C and 1000 degrees C were investigated. The slopes of the higher-order resonance dips of the TLPFG and CLPFG corresponded to 0.119 nm degrees C-1 and 0.09 nm degrees C-1, respectively, during the heating process, and to 0.116 degrees C-1 and 0.09 nm degrees C-1, respectively, during the cooling process. In the low and high temperature zones, the TLPFG exhibited higher sensitivity when compared to that of the CLPFG, while the CLPFG exhibited higher sensing precision with linearity approaching 1. Given the simple and unsophisticated fabrication process and the high quality and sensitivity of the fabricated gratings, the proposed sensors can play an important role in high-precision temperature-sensing applications.